NaiveBayes/GaussianNB.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 朴素贝叶斯\n",
    "\n",
    "基于贝叶斯定理与特征条件独立假设的分类方法。\n",
    "\n",
    "模型：\n",
    "\n",
    "- 高斯模型\n",
    "- 多项式模型\n",
    "- 伯努利模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "from collections import Counter\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# data\n",
    "def create_data():\n",
    "    iris = load_iris()\n",
    "    df = pd.DataFrame(iris.data, columns=iris.feature_names)\n",
    "    df['label'] = iris.target\n",
    "    df.columns = ['sepal length', 'sepal width', 'petal length', 'petal width', 'label']\n",
    "    data = np.array(df.iloc[:100, :])\n",
    "    # print(data)\n",
    "    return data[:,:-1], data[:,-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = create_data()\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 4.8,  3. ,  1.4,  0.1]), 0.0)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test[0], y_test[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "参考：https://machinelearningmastery.com/naive-bayes-classifier-scratch-python/\n",
    "\n",
    "## GaussianNB 高斯朴素贝叶斯\n",
    "\n",
    "特征的可能性被假设为高斯\n",
    "\n",
    "概率密度函数：\n",
    "$$P(x_i | y_k)=\\frac{1}{\\sqrt{2\\pi\\sigma^2_{yk}}}exp(-\\frac{(x_i-\\mu_{yk})^2}{2\\sigma^2_{yk}})$$\n",
    "\n",
    "数学期望(mean)：$\\mu$，方差：$\\sigma^2=\\frac{\\sum(X-\\mu)^2}{N}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class NaiveBayes:\n",
    "    def __init__(self):\n",
    "        self.model = None\n",
    "\n",
    "    # 数学期望\n",
    "    @staticmethod\n",
    "    def mean(X):\n",
    "        return sum(X) / float(len(X))\n",
    "\n",
    "    # 标准差（方差）\n",
    "    def stdev(self, X):\n",
    "        avg = self.mean(X)\n",
    "        return math.sqrt(sum([pow(x-avg, 2) for x in X]) / float(len(X)))\n",
    "\n",
    "    # 概率密度函数\n",
    "    def gaussian_probability(self, x, mean, stdev):\n",
    "        exponent = math.exp(-(math.pow(x-mean,2)/(2*math.pow(stdev,2))))\n",
    "        return (1 / (math.sqrt(2*math.pi) * stdev)) * exponent\n",
    "\n",
    "    # 处理X_train\n",
    "    def summarize(self, train_data):\n",
    "        summaries = [(self.mean(i), self.stdev(i)) for i in zip(*train_data)]\n",
    "        return summaries\n",
    "\n",
    "    # 分类别求出数学期望和标准差\n",
    "    def fit(self, X, y):\n",
    "        labels = list(set(y))\n",
    "        data = {label:[] for label in labels}\n",
    "        for f, label in zip(X, y):\n",
    "            data[label].append(f)\n",
    "        self.model = {label: self.summarize(value) for label, value in data.items()}\n",
    "        return 'gaussianNB train done!'\n",
    "\n",
    "    # 计算概率\n",
    "    def calculate_probabilities(self, input_data):\n",
    "        # summaries:{0.0: [(5.0, 0.37),(3.42, 0.40)], 1.0: [(5.8, 0.449),(2.7, 0.27)]}\n",
    "        # input_data:[1.1, 2.2]\n",
    "        probabilities = {}\n",
    "        for label, value in self.model.items():\n",
    "            probabilities[label] = 1\n",
    "            for i in range(len(value)):\n",
    "                mean, stdev = value[i]\n",
    "                probabilities[label] *= self.gaussian_probability(input_data[i], mean, stdev)\n",
    "        return probabilities\n",
    "\n",
    "    # 类别\n",
    "    def predict(self, X_test):\n",
    "        # {0.0: 2.9680340789325763e-27, 1.0: 3.5749783019849535e-26}\n",
    "        label = sorted(self.calculate_probabilities(X_test).items(), key=lambda x: x[-1])[-1][0]\n",
    "        return label\n",
    "\n",
    "    def score(self, X_test, y_test):\n",
    "        right = 0\n",
    "        for X, y in zip(X_test, y_test):\n",
    "            label = self.predict(X)\n",
    "            if label == y:\n",
    "                right += 1\n",
    "\n",
    "        return right / float(len(X_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = NaiveBayes()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'gaussianNB train done!'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n"
     ]
    }
   ],
   "source": [
    "print(model.predict([4.4,  3.2,  1.3,  0.2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "scikit-learn实例\n",
    "\n",
    "# sklearn.naive_bayes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.naive_bayes import GaussianNB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GaussianNB(priors=None)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf = GaussianNB()\n",
    "clf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "E:\\Anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:395: DeprecationWarning: Passing 1d arrays as data is deprecated in 0.17 and will raise ValueError in 0.19. Reshape your data either using X.reshape(-1, 1) if your data has a single feature or X.reshape(1, -1) if it contains a single sample.\n",
      "  DeprecationWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf.predict([4.4,  3.2,  1.3,  0.2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.naive_bayes import BernoulliNB, MultinomialNB # 伯努利模型和多项式模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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